First of all, A big WELCOME to my dearest teammates:
It is an honor to meet you all and I am really looking forward to our collaboration on this game.
Back to the topic. The purpose of this notebook is to provide insights of the data sets that we are going to use to in this competition, thus I will explore the dataset in as much details as I can and hopefully by the end of this notebook, I can clear some of your doubts and you have a really good grasp of what we are about to deal with in this game.
A few things to keep in mind before we dive in:
As the participants of this competition, we are provided with four files, namely:
The two files that are marked red are the ones that we need to work with, we will look into them in more details in the later part of this notebook. As for the other two example files, the organizer put them there to give us an idea of what test sets look like. Since in this competition the testing and evaulation will be done by the organizers, we can completely ignor these two files for now.
(This is the section of blocks where I include all the modules that I will need in my codes. Just one little habbit of mine, I feel it is easier to handle your code in this way)
#Import section
import numpy as np
import pandas as pd
import seaborn as sns
import os
import re
import matplotlib.pyplot as plt
import datatable as dt
# You might not have this package installed on your own computer.
# But you can simply run pip install command to install it.
# datatable is for loading large size files. Since we have a 5GB data file in this game, it's a good idea to load it
# in dt first and then transform into pandas dataframe.
# Check if you have all the files you need under your working directory
# You should see all four csv files mentioned above
fileNames = os.listdir()
print('File names: ')
for file in fileNames:
if re.match('[a-zA-Z_]*.csv',file):
print(' [+]'+file)
File names: [+]example_sample_submission.csv [+]train.csv [+]example_test.csv [+]features.csv
This is the section where we really set our foot in the door.
This competition is evaluated on a utility score.
Each row in the test set represents a trading opportunity for which you will be predicting an action value:
Each trade j has an associated **weight** and **resp**, which represents a return.
For each date i, we define:
$$P_{i} = {\sum weight_{ij} * resp_{}*action_{ij}}.$$$$ t = {\sum P_{i} \over \sqrt{\sum P_{i}^2}} * \sqrt{250\over|i|}$$where (|i|) is the number of unique dates in the test set. The utility is then defined as: $$ U = min(max(t, 0), 6)*{\sum p_{i}} $$
Our goal is to maximize the utility score.
In order to do that we need a criterion for determining the value of action.
For example like what most of people did:
- action = 1 when resp (return) > 0
- action = 0 otherwise
This is the dataset that we are going to use to train our model.
Size:
2390491 rows x 138 columns
Columns:
Unfortunately, all the features are anonymous meaning there is no way to know extractly what they are. Although we can make some deductions or presumptions on these features based on their distributions, null value patterns and tag structure, I am afraid that finance hardly plays a role in this competition.
Anyway, let's take a look into the dataset.
# Load in files
df_train = dt.fread('train.csv')
df_train = df_train.to_pandas()
# Head view
df_train.head()
| date | weight | resp_1 | resp_2 | resp_3 | resp_4 | resp | feature_0 | feature_1 | feature_2 | ... | feature_121 | feature_122 | feature_123 | feature_124 | feature_125 | feature_126 | feature_127 | feature_128 | feature_129 | ts_id | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0.000000 | 0.009916 | 0.014079 | 0.008773 | 0.001390 | 0.006270 | 1 | -1.872746 | -2.191242 | ... | NaN | 1.168391 | 8.313583 | 1.782433 | 14.018213 | 2.653056 | 12.600292 | 2.301488 | 11.445807 | 0 |
| 1 | 0 | 16.673515 | -0.002828 | -0.003226 | -0.007319 | -0.011114 | -0.009792 | -1 | -1.349537 | -1.704709 | ... | NaN | -1.178850 | 1.777472 | -0.915458 | 2.831612 | -1.417010 | 2.297459 | -1.304614 | 1.898684 | 1 |
| 2 | 0 | 0.000000 | 0.025134 | 0.027607 | 0.033406 | 0.034380 | 0.023970 | -1 | 0.812780 | -0.256156 | ... | NaN | 6.115747 | 9.667908 | 5.542871 | 11.671595 | 7.281757 | 10.060014 | 6.638248 | 9.427299 | 2 |
| 3 | 0 | 0.000000 | -0.004730 | -0.003273 | -0.000461 | -0.000476 | -0.003200 | -1 | 1.174378 | 0.344640 | ... | NaN | 2.838853 | 0.499251 | 3.033732 | 1.513488 | 4.397532 | 1.266037 | 3.856384 | 1.013469 | 3 |
| 4 | 0 | 0.138531 | 0.001252 | 0.002165 | -0.001215 | -0.006219 | -0.002604 | 1 | -3.172026 | -3.093182 | ... | NaN | 0.344850 | 4.101145 | 0.614252 | 6.623456 | 0.800129 | 5.233243 | 0.362636 | 3.926633 | 4 |
5 rows × 138 columns
#Tail view
df_train.tail()
| date | weight | resp_1 | resp_2 | resp_3 | resp_4 | resp | feature_0 | feature_1 | feature_2 | ... | feature_121 | feature_122 | feature_123 | feature_124 | feature_125 | feature_126 | feature_127 | feature_128 | feature_129 | ts_id | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2390486 | 499 | 0.000000 | 0.000142 | 0.000142 | 0.005829 | 0.020342 | 0.015396 | 1 | -1.649365 | -1.169996 | ... | -1.896874 | -1.260055 | 1.947725 | -1.994399 | -1.685163 | -2.866165 | -0.216130 | -1.892048 | 0.901585 | 2390486 |
| 2390487 | 499 | 0.000000 | 0.000012 | 0.000012 | -0.000935 | -0.006326 | -0.004718 | 1 | 2.432943 | 5.284504 | ... | -0.936553 | 1.064936 | 3.119762 | -0.419796 | -0.208975 | -0.146749 | 0.730166 | 0.648452 | 2.068737 | 2390487 |
| 2390488 | 499 | 0.000000 | 0.000499 | 0.000499 | 0.007605 | 0.024907 | 0.016591 | 1 | -0.622475 | -0.963682 | ... | -2.956745 | -0.640334 | -2.279663 | -0.950259 | -4.388417 | -1.669922 | -3.288939 | -1.336142 | -2.814239 | 2390488 |
| 2390489 | 499 | 0.283405 | -0.000156 | -0.000156 | -0.001375 | -0.003702 | -0.002004 | -1 | -1.463757 | -1.107228 | ... | -2.035894 | -1.780962 | 0.881246 | -2.202140 | -1.912601 | -3.341684 | -0.571188 | -2.185795 | 0.627452 | 2390489 |
| 2390490 | 499 | 0.000000 | -0.001855 | -0.001855 | -0.001194 | -0.000864 | -0.001905 | -1 | -1.817184 | -1.131577 | ... | -0.571013 | 2.483421 | 8.284037 | -0.698486 | 0.199953 | -0.168395 | 2.051091 | 1.726072 | 5.823676 | 2390490 |
5 rows × 138 columns
Now that we have viewed what the data are like, the next thing we care about is whether or not the dataset contains missing value for obvious reasons: defective data are not helpful at all in training our models.
And this leads to our next question: how do we handle the missing values? There are many different ways to handle missing data. Here I will list three most commom ways:
For now, I will just stop here and leave this question to our discussion.
Now, Let's take a close look at those null value.
# Calculating how many null/missing values in each columns
pd.DataFrame(df_train.isnull().sum())
| 0 | |
|---|---|
| date | 0 |
| weight | 0 |
| resp_1 | 0 |
| resp_2 | 0 |
| resp_3 | 0 |
| ... | ... |
| feature_126 | 8853 |
| feature_127 | 8853 |
| feature_128 | 1921 |
| feature_129 | 1921 |
| ts_id | 0 |
138 rows × 1 columns
# Same as above except in percentage this time
cm = sns.light_palette("red", as_cmap=True)
pd.DataFrame(df_train.isnull().sum()/2390491).style.background_gradient(cmap=cm)
| 0 | |
|---|---|
| date | 0.000000 |
| weight | 0.000000 |
| resp_1 | 0.000000 |
| resp_2 | 0.000000 |
| resp_3 | 0.000000 |
| resp_4 | 0.000000 |
| resp | 0.000000 |
| feature_0 | 0.000000 |
| feature_1 | 0.000000 |
| feature_2 | 0.000000 |
| feature_3 | 0.000187 |
| feature_4 | 0.000187 |
| feature_5 | 0.000000 |
| feature_6 | 0.000000 |
| feature_7 | 0.164458 |
| feature_8 | 0.164458 |
| feature_9 | 0.000330 |
| feature_10 | 0.000330 |
| feature_11 | 0.033472 |
| feature_12 | 0.033472 |
| feature_13 | 0.006423 |
| feature_14 | 0.006423 |
| feature_15 | 0.002796 |
| feature_16 | 0.002796 |
| feature_17 | 0.165462 |
| feature_18 | 0.165462 |
| feature_19 | 0.000330 |
| feature_20 | 0.000330 |
| feature_21 | 0.034070 |
| feature_22 | 0.034070 |
| feature_23 | 0.006423 |
| feature_24 | 0.006423 |
| feature_25 | 0.002796 |
| feature_26 | 0.002796 |
| feature_27 | 0.165462 |
| feature_28 | 0.165462 |
| feature_29 | 0.000330 |
| feature_30 | 0.000330 |
| feature_31 | 0.034070 |
| feature_32 | 0.034070 |
| feature_33 | 0.006423 |
| feature_34 | 0.006423 |
| feature_35 | 0.002796 |
| feature_36 | 0.002796 |
| feature_37 | 0.000000 |
| feature_38 | 0.000000 |
| feature_39 | 0.000000 |
| feature_40 | 0.000000 |
| feature_41 | 0.000000 |
| feature_42 | 0.000000 |
| feature_43 | 0.000000 |
| feature_44 | 0.000187 |
| feature_45 | 0.000187 |
| feature_46 | 0.000000 |
| feature_47 | 0.000000 |
| feature_48 | 0.000000 |
| feature_49 | 0.000000 |
| feature_50 | 0.000000 |
| feature_51 | 0.000000 |
| feature_52 | 0.000000 |
| feature_53 | 0.000000 |
| feature_54 | 0.000000 |
| feature_55 | 0.028617 |
| feature_56 | 0.000301 |
| feature_57 | 0.000000 |
| feature_58 | 0.000000 |
| feature_59 | 0.000020 |
| feature_60 | 0.000000 |
| feature_61 | 0.000000 |
| feature_62 | 0.000000 |
| feature_63 | 0.000000 |
| feature_64 | 0.000000 |
| feature_65 | 0.000000 |
| feature_66 | 0.000000 |
| feature_67 | 0.000000 |
| feature_68 | 0.000000 |
| feature_69 | 0.000000 |
| feature_70 | 0.000000 |
| feature_71 | 0.000000 |
| feature_72 | 0.147010 |
| feature_73 | 0.000330 |
| feature_74 | 0.026810 |
| feature_75 | 0.006423 |
| feature_76 | 0.002796 |
| feature_77 | 0.000000 |
| feature_78 | 0.147010 |
| feature_79 | 0.000330 |
| feature_80 | 0.026810 |
| feature_81 | 0.006423 |
| feature_82 | 0.002796 |
| feature_83 | 0.000000 |
| feature_84 | 0.147010 |
| feature_85 | 0.000330 |
| feature_86 | 0.026810 |
| feature_87 | 0.006423 |
| feature_88 | 0.002796 |
| feature_89 | 0.000000 |
| feature_90 | 0.147010 |
| feature_91 | 0.000330 |
| feature_92 | 0.026810 |
| feature_93 | 0.006423 |
| feature_94 | 0.002796 |
| feature_95 | 0.000000 |
| feature_96 | 0.147010 |
| feature_97 | 0.000330 |
| feature_98 | 0.026810 |
| feature_99 | 0.006423 |
| feature_100 | 0.002796 |
| feature_101 | 0.000000 |
| feature_102 | 0.147010 |
| feature_103 | 0.000330 |
| feature_104 | 0.026810 |
| feature_105 | 0.006423 |
| feature_106 | 0.002796 |
| feature_107 | 0.000000 |
| feature_108 | 0.147010 |
| feature_109 | 0.000330 |
| feature_110 | 0.026810 |
| feature_111 | 0.006423 |
| feature_112 | 0.002796 |
| feature_113 | 0.000000 |
| feature_114 | 0.147010 |
| feature_115 | 0.000330 |
| feature_116 | 0.026810 |
| feature_117 | 0.006423 |
| feature_118 | 0.002796 |
| feature_119 | 0.000000 |
| feature_120 | 0.029222 |
| feature_121 | 0.029222 |
| feature_122 | 0.000093 |
| feature_123 | 0.000093 |
| feature_124 | 0.006728 |
| feature_125 | 0.006728 |
| feature_126 | 0.003703 |
| feature_127 | 0.003703 |
| feature_128 | 0.000804 |
| feature_129 | 0.000804 |
| ts_id | 0.000000 |
Note that some features have severe issue with missing values (the red ones). On top of that, it's even more interesting to discover that same number of missing values are found across different features (e.g 7 vs 8; 17 vs 18; 27 vs 28 )
Now let's filter out these features (severe ones) and see what we can find.
null_percentage = df_train.isnull().sum()/2390491
null_percentage_mask = null_percentage > 0.1
filter_features = pd.DataFrame(null_percentage[null_percentage_mask],columns = ['Null value percentage'])
filter_features
| Null value percentage | |
|---|---|
| feature_7 | 0.164458 |
| feature_8 | 0.164458 |
| feature_17 | 0.165462 |
| feature_18 | 0.165462 |
| feature_27 | 0.165462 |
| feature_28 | 0.165462 |
| feature_72 | 0.147010 |
| feature_78 | 0.147010 |
| feature_84 | 0.147010 |
| feature_90 | 0.147010 |
| feature_96 | 0.147010 |
| feature_102 | 0.147010 |
| feature_108 | 0.147010 |
| feature_114 | 0.147010 |
# Features with more than 10% missing value
filter_features.index
Index(['feature_7', 'feature_8', 'feature_17', 'feature_18', 'feature_27',
'feature_28', 'feature_72', 'feature_78', 'feature_84', 'feature_90',
'feature_96', 'feature_102', 'feature_108', 'feature_114'],
dtype='object')
df_train[list(filter_features.index)]
| feature_7 | feature_8 | feature_17 | feature_18 | feature_27 | feature_28 | feature_72 | feature_78 | feature_84 | feature_90 | feature_96 | feature_102 | feature_108 | feature_114 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 1 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 2 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 3 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 4 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 2390486 | 0.526201 | 1.162469 | 0.928914 | 2.150500 | -0.041265 | -0.149770 | -0.539591 | -2.627014 | -0.193006 | 1.689489 | 0.104432 | 2.754382 | -0.128550 | 2.107612 |
| 2390487 | -0.064645 | 0.163244 | 0.170509 | 0.526144 | -1.301215 | -3.244589 | 1.752626 | 1.352782 | 2.578997 | 0.893971 | 2.297062 | 0.614411 | 3.295566 | 0.719010 |
| 2390488 | 0.140248 | 0.039213 | 0.437936 | 0.443755 | -0.013002 | -0.004482 | 0.213130 | 0.316766 | 0.206049 | -0.073920 | 0.108439 | -0.248634 | 0.217940 | -0.174350 |
| 2390489 | -0.683812 | -0.939522 | -0.968833 | -1.735649 | 0.026421 | 0.049269 | -0.523474 | -3.177544 | 0.875750 | 6.022596 | 1.157290 | 7.345104 | 1.492829 | 6.529618 |
| 2390490 | 0.198607 | 0.752480 | -0.163660 | -0.477443 | 0.601387 | 1.804146 | 0.525496 | 0.580039 | 0.025297 | -0.658249 | -0.372650 | -1.277911 | -0.298838 | -0.927916 |
2390491 rows × 14 columns
In the training set, train.csv, you are provided a resp value, as well as several other resp_{1,2,3,4} values that represent returns over different time horizons.
And as you will see, as i --> larger; resp_i --> less volatility, and return tends to be stable during 100th - 200th day
#Head view of returns
df_train[['resp','resp_1','resp_2','resp_3']].head()
| resp | resp_1 | resp_2 | resp_3 | |
|---|---|---|---|---|
| 0 | 0.006270 | 0.009916 | 0.014079 | 0.008773 |
| 1 | -0.009792 | -0.002828 | -0.003226 | -0.007319 |
| 2 | 0.023970 | 0.025134 | 0.027607 | 0.033406 |
| 3 | -0.003200 | -0.004730 | -0.003273 | -0.000461 |
| 4 | -0.002604 | 0.001252 | 0.002165 | -0.001215 |
fig, ax1 = plt.subplots(1,1,figsize = (15,8))
df_train_daily = df_train[['date','resp', 'resp_1','resp_2','resp_3','resp_4']].groupby('date').sum()
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp'], ax = ax1, color = 'red', label = 'resp')
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp_1'], ax = ax1, color = 'blue', label = 'resp_1')
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp_2'], ax = ax1, color = 'green', label = 'resp_2')
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp_3'], ax = ax1, color = 'orange', label = 'resp_3')
plt.title('Daily return', fontsize = 20)
Text(0.5, 1.0, 'Daily return')
fig, ax1 = plt.subplots(1,1,figsize = (15,8))
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp'].cumsum(), ax = ax1, color = 'red',label = 'resp')
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp_1'].cumsum(), ax = ax1, color = 'blue', label = 'resp_1')
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp_2'].cumsum(), ax = ax1, color = 'green', label = 'resp_2')
sns.lineplot(x = df_train_daily.index, y = df_train_daily['resp_3'].cumsum(), ax = ax1, color = 'purple', label = 'resp_3')
plt.title('Cumulative returns', fontsize = 20)
Text(0.5, 1.0, 'Cumulative returns')
In my opinion, the key to win this game = right features + right model
Feature reduction/selection is an important in this competition.
We will need to discuss which features to drop.
In this section, I will show some visualizations of features' distributions and correlations. While some of their distributions have interesting shapes while the correlations are rather equal among all the features. Again, it proves the need of features processing.
# Plotting (Do not run this, it takes long time)
fig, ax = plt.subplots(13,10, figsize = (52,40))
for i in range(13):
for j in range(10):
index = 10*i+j
sns.distplot(df_train['feature_'+str(index)], ax = ax[i,j])
# visualization of distributions of features
fig.tight_layout(pad=2.0)
fig
# Visualization of the correlation matrix
cm = sns.diverging_palette(5, 250, as_cmap=True)
mask_ut=np.triu(np.ones(df_train.shape)).astype(np.bool)
df_train_corr = df_train.corr()
df_train_corr.style.background_gradient(cmap=cm, axis=None,).set_precision(2)
| date | weight | resp_1 | resp_2 | resp_3 | resp_4 | resp | feature_0 | feature_1 | feature_2 | feature_3 | feature_4 | feature_5 | feature_6 | feature_7 | feature_8 | feature_9 | feature_10 | feature_11 | feature_12 | feature_13 | feature_14 | feature_15 | feature_16 | feature_17 | feature_18 | feature_19 | feature_20 | feature_21 | feature_22 | feature_23 | feature_24 | feature_25 | feature_26 | feature_27 | feature_28 | feature_29 | feature_30 | feature_31 | feature_32 | feature_33 | feature_34 | feature_35 | feature_36 | feature_37 | feature_38 | feature_39 | feature_40 | feature_41 | feature_42 | feature_43 | feature_44 | feature_45 | feature_46 | feature_47 | feature_48 | feature_49 | feature_50 | feature_51 | feature_52 | feature_53 | feature_54 | feature_55 | feature_56 | feature_57 | feature_58 | feature_59 | feature_60 | feature_61 | feature_62 | feature_63 | feature_64 | feature_65 | feature_66 | feature_67 | feature_68 | feature_69 | feature_70 | feature_71 | feature_72 | feature_73 | feature_74 | feature_75 | feature_76 | feature_77 | feature_78 | feature_79 | feature_80 | feature_81 | feature_82 | feature_83 | feature_84 | feature_85 | feature_86 | feature_87 | feature_88 | feature_89 | feature_90 | feature_91 | feature_92 | feature_93 | feature_94 | feature_95 | feature_96 | feature_97 | feature_98 | feature_99 | feature_100 | feature_101 | feature_102 | feature_103 | feature_104 | feature_105 | feature_106 | feature_107 | feature_108 | feature_109 | feature_110 | feature_111 | feature_112 | feature_113 | feature_114 | feature_115 | feature_116 | feature_117 | feature_118 | feature_119 | feature_120 | feature_121 | feature_122 | feature_123 | feature_124 | feature_125 | feature_126 | feature_127 | feature_128 | feature_129 | ts_id | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| date | 1.00 | 0.03 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | 0.00 | -0.03 | 0.02 | -0.00 | -0.00 | -0.01 | -0.01 | -0.01 | -0.00 | -0.05 | 0.00 | -0.02 | 0.00 | -0.03 | 0.00 | -0.04 | 0.01 | -0.01 | 0.00 | -0.02 | -0.01 | -0.01 | -0.00 | -0.02 | -0.00 | -0.02 | -0.01 | -0.01 | -0.00 | -0.03 | -0.01 | -0.01 | -0.00 | -0.02 | -0.01 | -0.02 | -0.01 | -0.00 | -0.00 | -0.00 | -0.00 | 0.03 | -0.03 | -0.13 | -0.08 | -0.14 | -0.05 | -0.06 | -0.02 | 0.01 | -0.05 | 0.01 | -0.01 | -0.06 | -0.04 | -0.09 | -0.06 | -0.08 | -0.08 | -0.07 | -0.02 | -0.02 | -0.01 | -0.01 | -0.04 | -0.02 | -0.02 | -0.04 | -0.04 | -0.03 | -0.01 | 0.02 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.01 | -0.01 | 0.01 | -0.00 | 0.00 | 0.01 | -0.03 | -0.09 | -0.03 | -0.06 | -0.05 | -0.03 | -0.10 | -0.01 | 0.02 | -0.00 | 0.01 | 0.01 | -0.03 | -0.09 | -0.02 | -0.06 | -0.05 | -0.03 | -0.10 | -0.02 | 0.03 | -0.00 | 0.01 | 0.02 | -0.03 | -0.09 | -0.04 | -0.07 | -0.06 | -0.05 | -0.10 | -0.06 | -0.04 | -0.05 | -0.04 | -0.06 | -0.04 | -0.05 | -0.04 | -0.05 | -0.04 | 1.00 |
| weight | 0.03 | 1.00 | -0.02 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | 0.06 | -0.00 | -0.00 | -0.00 | -0.00 | -0.02 | -0.00 | -0.06 | 0.02 | -0.03 | 0.00 | -0.04 | 0.01 | -0.05 | 0.02 | -0.01 | -0.00 | -0.03 | -0.01 | -0.01 | -0.00 | -0.01 | 0.00 | -0.02 | -0.00 | -0.01 | 0.00 | -0.03 | -0.00 | -0.01 | 0.01 | -0.01 | 0.01 | -0.02 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.34 | -0.21 | -0.17 | -0.01 | 0.06 | 0.08 | 0.06 | 0.07 | 0.08 | 0.22 | 0.54 | 0.28 | -0.18 | 0.02 | -0.00 | -0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.00 | -0.00 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | -0.01 | 0.25 | 0.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | -0.04 | -0.04 | -0.04 | -0.04 | -0.04 | -0.03 | 0.05 | 0.03 | 0.04 | 0.04 | 0.03 | 0.07 | -0.04 | -0.04 | -0.04 | -0.04 | -0.04 | -0.03 | 0.06 | 0.02 | 0.04 | 0.03 | 0.02 | 0.07 | -0.05 | -0.05 | -0.05 | -0.05 | -0.06 | -0.03 | 0.05 | 0.06 | 0.05 | 0.05 | 0.05 | 0.06 | -0.21 | -0.02 | -0.20 | -0.01 | -0.21 | -0.02 | -0.22 | -0.01 | -0.21 | -0.01 | 0.03 |
| resp_1 | -0.01 | -0.02 | 1.00 | 0.89 | 0.68 | 0.36 | 0.45 | -0.01 | 0.05 | 0.04 | 0.02 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.04 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 | 0.04 | 0.03 | 0.00 | 0.01 | 0.02 | 0.02 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.04 | 0.03 | 0.03 | 0.02 | 0.04 | 0.02 | 0.03 | 0.02 | 0.03 | 0.02 | -0.00 | 0.00 | 0.03 | 0.02 | -0.01 | 0.02 | 0.02 | 0.01 | 0.00 | -0.01 | -0.00 | -0.01 | -0.01 | -0.01 | -0.02 | -0.02 | 0.04 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.01 | -0.00 | -0.01 | -0.01 | 0.05 | 0.03 | 0.04 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.01 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | 0.03 | 0.01 | 0.04 | 0.02 | 0.03 | 0.01 | 0.03 | 0.01 | 0.04 | 0.01 | -0.01 |
| resp_2 | -0.01 | -0.01 | 0.89 | 1.00 | 0.82 | 0.47 | 0.60 | -0.01 | 0.04 | 0.03 | 0.02 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 | 0.03 | 0.02 | 0.03 | 0.02 | -0.01 | 0.00 | 0.00 | 0.01 | -0.01 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.04 | 0.03 | 0.03 | 0.02 | 0.04 | 0.03 | 0.04 | 0.02 | 0.03 | 0.02 | -0.01 | -0.00 | 0.03 | 0.02 | -0.01 | 0.02 | 0.02 | 0.01 | 0.00 | -0.01 | -0.00 | -0.01 | -0.01 | -0.01 | -0.02 | -0.02 | 0.04 | 0.02 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.01 | -0.01 | 0.04 | 0.02 | 0.03 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.01 | 0.00 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.03 | 0.01 | 0.03 | 0.01 | 0.03 | 0.01 | 0.03 | 0.01 | 0.03 | 0.01 | -0.01 |
| resp_3 | -0.01 | -0.01 | 0.68 | 0.82 | 1.00 | 0.81 | 0.82 | -0.00 | 0.03 | 0.02 | -0.00 | -0.00 | 0.02 | 0.01 | 0.02 | 0.01 | 0.03 | 0.02 | 0.02 | 0.02 | 0.02 | 0.01 | 0.02 | 0.01 | -0.00 | 0.00 | 0.01 | 0.01 | -0.00 | -0.00 | -0.00 | 0.00 | 0.01 | 0.01 | 0.02 | 0.02 | 0.01 | 0.01 | 0.03 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 | -0.01 | -0.00 | 0.01 | 0.01 | -0.01 | 0.02 | 0.01 | 0.01 | 0.00 | -0.00 | 0.00 | -0.00 | -0.01 | -0.00 | -0.01 | -0.01 | 0.03 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.01 | -0.01 | 0.03 | 0.01 | 0.02 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.01 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.01 | 0.01 | 0.00 | 0.00 | -0.00 | -0.00 | 0.01 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.01 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.02 | 0.00 | 0.02 | 0.01 | 0.02 | 0.00 | 0.02 | 0.00 | 0.02 | 0.01 | -0.01 |
| resp_4 | -0.01 | -0.01 | 0.36 | 0.47 | 0.81 | 1.00 | 0.96 | -0.01 | 0.02 | 0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.02 | 0.01 | 0.02 | 0.01 | 0.02 | 0.01 | 0.02 | 0.01 | 0.02 | 0.01 | -0.02 | -0.01 | -0.00 | -0.00 | -0.02 | -0.01 | -0.02 | -0.01 | -0.01 | -0.00 | 0.03 | 0.02 | 0.02 | 0.01 | 0.03 | 0.02 | 0.03 | 0.02 | 0.02 | 0.01 | -0.02 | -0.01 | 0.02 | 0.02 | -0.01 | 0.02 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.01 | -0.01 | 0.02 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.01 | 0.00 | 0.01 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.01 | -0.00 | 0.01 | -0.00 | 0.00 | 0.00 | -0.01 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.01 | -0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.01 | -0.01 | 0.00 | -0.00 | -0.00 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.01 | 0.02 | -0.00 | 0.02 | 0.00 | 0.02 | -0.00 | 0.02 | -0.00 | 0.02 | 0.00 | -0.01 |
| resp | -0.01 | -0.01 | 0.45 | 0.60 | 0.82 | 0.96 | 1.00 | -0.02 | 0.02 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.01 | 0.02 | 0.01 | 0.02 | 0.01 | 0.02 | 0.01 | 0.02 | 0.01 | -0.03 | -0.02 | -0.01 | -0.01 | -0.03 | -0.02 | -0.02 | -0.02 | -0.02 | -0.01 | 0.05 | 0.03 | 0.03 | 0.02 | 0.05 | 0.03 | 0.04 | 0.02 | 0.03 | 0.02 | -0.03 | -0.02 | 0.04 | 0.03 | -0.01 | 0.02 | 0.02 | 0.01 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.01 | -0.01 | -0.01 | 0.02 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.02 | 0.00 | 0.01 | -0.00 | 0.01 | -0.00 | 0.00 | 0.01 | -0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | -0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | -0.01 | 0.01 | 0.00 | -0.00 | 0.01 | 0.00 | -0.01 | 0.00 | -0.00 | -0.01 | 0.01 | 0.01 | 0.00 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.01 | 0.02 | -0.00 | 0.02 | 0.00 | 0.02 | -0.00 | 0.02 | 0.00 | 0.02 | 0.00 | -0.01 |
| feature_0 | 0.00 | -0.01 | -0.01 | -0.01 | -0.00 | -0.01 | -0.02 | 1.00 | 0.02 | 0.02 | -0.02 | -0.01 | -0.01 | 0.03 | -0.02 | -0.01 | 0.03 | 0.03 | -0.01 | -0.00 | 0.02 | 0.02 | 0.03 | 0.03 | 0.66 | 0.67 | 0.69 | 0.73 | 0.71 | 0.63 | 0.70 | 0.71 | 0.71 | 0.73 | -0.65 | -0.67 | -0.71 | -0.74 | -0.66 | -0.69 | -0.69 | -0.67 | -0.73 | -0.73 | 0.72 | 0.74 | -0.71 | -0.75 | -0.01 | 0.01 | 0.01 | -0.01 | -0.00 | 0.02 | 0.02 | 0.02 | 0.01 | 0.02 | 0.00 | -0.01 | 0.02 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.01 | -0.01 | 0.01 | 0.01 | -0.00 | 0.03 | 0.02 | -0.04 | -0.04 | 0.03 | 0.02 | 0.02 | -0.12 | -0.58 | -0.22 | -0.37 | -0.53 | -0.02 | -0.13 | -0.52 | -0.20 | -0.35 | -0.45 | -0.02 | -0.04 | -0.51 | -0.10 | -0.29 | -0.45 | -0.01 | -0.05 | -0.52 | -0.11 | -0.22 | -0.36 | -0.01 | 0.06 | 0.52 | 0.15 | 0.23 | 0.41 | -0.00 | 0.06 | 0.44 | 0.11 | 0.22 | 0.41 | 0.00 | 0.01 | 0.02 | 0.01 | 0.01 | 0.02 | -0.00 | 0.01 | 0.02 | 0.01 | 0.01 | 0.02 | -0.00 | 0.01 | 0.00 | 0.02 | 0.00 | 0.01 | -0.00 | 0.01 | 0.00 | 0.02 | 0.00 | 0.00 |
| feature_1 | -0.03 | -0.01 | 0.05 | 0.04 | 0.03 | 0.02 | 0.02 | 0.02 | 1.00 | 0.86 | 0.01 | 0.01 | 0.00 | -0.00 | 0.12 | 0.08 | 0.72 | 0.58 | 0.22 | 0.16 | 0.39 | 0.28 | 0.62 | 0.49 | 0.12 | 0.08 | 0.27 | 0.22 | 0.15 | 0.12 | 0.20 | 0.16 | 0.24 | 0.20 | 0.06 | 0.04 | 0.21 | 0.16 | 0.10 | 0.08 | 0.15 | 0.12 | 0.17 | 0.15 | 0.05 | 0.03 | 0.00 | -0.00 | -0.32 | 0.44 | 0.33 | 0.02 | -0.17 | 0.23 | 0.47 | 0.30 | 0.17 | 0.08 | -0.01 | -0.15 | 0.46 | 0.07 | 0.07 | 0.06 | 0.07 | 0.07 | 0.06 | 0.02 | 0.02 | 0.03 | 0.03 | 0.00 | -0.02 | -0.02 | -0.02 | -0.02 | 0.91 | 0.54 | 0.75 | -0.01 | -0.04 | -0.01 | -0.03 | -0.04 | -0.03 | -0.00 | -0.04 | -0.01 | -0.02 | -0.03 | -0.01 | 0.09 | 0.16 | 0.11 | 0.13 | 0.14 | 0.08 | -0.12 | 0.04 | -0.08 | -0.04 | 0.01 | -0.14 | 0.11 | 0.21 | 0.13 | 0.16 | 0.20 | 0.08 | -0.12 | 0.10 | -0.06 | -0.02 | 0.05 | -0.13 | 0.13 | 0.39 | 0.15 | 0.21 | 0.34 | 0.09 | -0.12 | 0.17 | -0.07 | -0.01 | 0.10 | -0.13 | 0.42 | -0.04 | 0.43 | -0.02 | 0.43 | -0.03 | 0.44 | -0.03 | 0.44 | -0.03 | -0.03 |
| feature_2 | 0.02 | 0.06 | 0.04 | 0.03 | 0.02 | 0.01 | 0.01 | 0.02 | 0.86 | 1.00 | 0.01 | 0.01 | -0.01 | -0.01 | 0.08 | 0.09 | 0.55 | 0.67 | 0.15 | 0.19 | 0.29 | 0.32 | 0.47 | 0.56 | 0.08 | 0.09 | 0.21 | 0.25 | 0.11 | 0.13 | 0.15 | 0.17 | 0.18 | 0.22 | 0.04 | 0.05 | 0.17 | 0.20 | 0.08 | 0.09 | 0.11 | 0.14 | 0.14 | 0.18 | 0.03 | 0.03 | 0.00 | 0.01 | -0.23 | 0.15 | -0.09 | 0.00 | -0.19 | 0.11 | 0.22 | 0.20 | 0.18 | 0.07 | 0.08 | -0.14 | 0.24 | 0.15 | 0.05 | 0.05 | 0.05 | 0.05 | 0.04 | 0.01 | 0.01 | 0.02 | 0.02 | -0.01 | -0.02 | -0.02 | -0.03 | -0.04 | 0.75 | 0.70 | 0.89 | -0.00 | -0.03 | -0.01 | -0.02 | -0.03 | 0.01 | 0.00 | -0.03 | -0.00 | -0.02 | -0.02 | 0.02 | 0.07 | 0.18 | 0.10 | 0.15 | 0.17 | 0.02 | -0.16 | 0.04 | -0.10 | -0.05 | 0.01 | -0.21 | 0.08 | 0.22 | 0.12 | 0.16 | 0.21 | 0.01 | -0.16 | 0.08 | -0.09 | -0.03 | 0.04 | -0.21 | 0.10 | 0.42 | 0.14 | 0.22 | 0.37 | 0.02 | -0.16 | 0.16 | -0.10 | -0.03 | 0.08 | -0.20 | 0.18 | 0.05 | 0.20 | 0.08 | 0.18 | 0.06 | 0.20 | 0.07 | 0.20 | 0.07 | 0.02 |
| feature_3 | -0.00 | -0.00 | 0.02 | 0.02 | -0.00 | -0.01 | 0.00 | -0.02 | 0.01 | 0.01 | 1.00 | 0.91 | 0.70 | 0.59 | 0.37 | 0.34 | 0.05 | 0.05 | 0.24 | 0.21 | 0.14 | 0.13 | 0.08 | 0.07 | 0.12 | 0.12 | 0.01 | 0.02 | 0.05 | 0.07 | 0.02 | 0.04 | 0.01 | 0.02 | 0.21 | 0.17 | 0.05 | 0.03 | 0.14 | 0.12 | 0.10 | 0.08 | 0.06 | 0.04 | 0.42 | 0.41 | 0.46 | 0.42 | -0.01 | 0.03 | 0.02 | -0.02 | -0.02 | 0.02 | 0.02 | 0.02 | 0.01 | 0.00 | 0.00 | -0.03 | 0.05 | 0.02 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 | -0.01 | -0.00 | -0.03 | -0.02 | 0.04 | 0.02 | 0.03 | -0.01 | 0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | 0.01 | -0.01 | -0.00 | 0.00 | -0.01 | -0.02 | 0.04 | -0.00 | 0.01 | 0.03 | -0.02 | -0.02 | 0.03 | -0.01 | 0.00 | 0.03 | -0.02 | -0.01 | 0.03 | 0.00 | 0.02 | 0.03 | -0.01 | -0.01 | 0.02 | -0.00 | 0.01 | 0.02 | -0.01 | -0.01 | 0.06 | 0.00 | 0.02 | 0.05 | -0.01 | -0.01 | 0.05 | -0.00 | 0.02 | 0.04 | -0.01 | 0.03 | -0.00 | 0.04 | 0.01 | 0.04 | 0.00 | 0.04 | 0.01 | 0.04 | 0.01 | -0.00 |
| feature_4 | -0.00 | -0.00 | 0.02 | 0.02 | -0.00 | -0.01 | 0.00 | -0.01 | 0.01 | 0.01 | 0.91 | 1.00 | 0.63 | 0.65 | 0.36 | 0.40 | 0.04 | 0.05 | 0.23 | 0.26 | 0.14 | 0.16 | 0.07 | 0.08 | 0.13 | 0.16 | 0.02 | 0.03 | 0.07 | 0.10 | 0.04 | 0.06 | 0.02 | 0.03 | 0.18 | 0.19 | 0.03 | 0.02 | 0.12 | 0.12 | 0.08 | 0.08 | 0.04 | 0.04 | 0.40 | 0.46 | 0.41 | 0.45 | -0.01 | 0.01 | -0.00 | -0.02 | -0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 0.01 | -0.02 | 0.03 | 0.03 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 | -0.01 | -0.01 | -0.02 | -0.02 | 0.03 | 0.02 | 0.04 | -0.01 | -0.00 | -0.01 | -0.01 | -0.00 | -0.01 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.01 | 0.03 | 0.00 | 0.01 | 0.03 | -0.01 | -0.01 | 0.03 | -0.00 | 0.01 | 0.03 | -0.02 | -0.01 | 0.03 | 0.01 | 0.02 | 0.03 | -0.01 | -0.01 | 0.03 | 0.01 | 0.02 | 0.03 | -0.01 | -0.00 | 0.06 | 0.01 | 0.03 | 0.05 | -0.01 | -0.01 | 0.05 | 0.01 | 0.03 | 0.04 | -0.01 | 0.01 | 0.00 | 0.02 | 0.02 | 0.02 | 0.01 | 0.02 | 0.01 | 0.02 | 0.02 | -0.00 |
| feature_5 | -0.01 | -0.00 | 0.02 | 0.02 | 0.02 | 0.00 | 0.00 | -0.01 | 0.00 | -0.01 | 0.70 | 0.63 | 1.00 | 0.91 | 0.28 | 0.25 | 0.04 | 0.03 | 0.18 | 0.16 | 0.11 | 0.09 | 0.06 | 0.04 | 0.08 | 0.11 | 0.01 | 0.04 | 0.03 | 0.07 | 0.01 | 0.04 | 0.00 | 0.03 | 0.18 | 0.12 | 0.04 | -0.00 | 0.12 | 0.07 | 0.08 | 0.04 | 0.05 | 0.01 | 0.29 | 0.32 | 0.35 | 0.29 | -0.01 | 0.03 | 0.02 | -0.02 | -0.02 | -0.00 | 0.02 | 0.01 | 0.00 | -0.01 | -0.01 | -0.03 | 0.04 | 0.02 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.02 | -0.01 | -0.00 | -0.02 | -0.02 | 0.03 | 0.01 | 0.02 | -0.01 | 0.00 | -0.01 | -0.01 | -0.00 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.00 | -0.00 | -0.02 | 0.03 | -0.01 | -0.00 | 0.02 | -0.02 | -0.02 | 0.03 | -0.01 | -0.00 | 0.02 | -0.02 | -0.01 | 0.02 | 0.00 | 0.01 | 0.03 | -0.01 | -0.02 | 0.02 | -0.00 | 0.01 | 0.02 | -0.02 | -0.01 | 0.04 | -0.00 | 0.02 | 0.04 | -0.02 | -0.02 | 0.04 | -0.00 | 0.01 | 0.03 | -0.02 | 0.03 | -0.00 | 0.04 | 0.01 | 0.03 | 0.00 | 0.03 | 0.00 | 0.03 | 0.01 | -0.01 |
| feature_6 | -0.01 | -0.00 | 0.02 | 0.02 | 0.01 | 0.00 | 0.00 | 0.03 | -0.00 | -0.01 | 0.59 | 0.65 | 0.91 | 1.00 | 0.25 | 0.28 | 0.03 | 0.03 | 0.16 | 0.17 | 0.09 | 0.10 | 0.04 | 0.04 | 0.11 | 0.15 | 0.03 | 0.06 | 0.07 | 0.11 | 0.04 | 0.08 | 0.03 | 0.06 | 0.12 | 0.10 | 0.00 | -0.03 | 0.07 | 0.05 | 0.04 | 0.02 | 0.01 | -0.02 | 0.29 | 0.36 | 0.26 | 0.25 | -0.00 | 0.01 | 0.01 | -0.02 | -0.02 | -0.00 | 0.01 | 0.00 | -0.00 | -0.01 | -0.00 | -0.02 | 0.03 | 0.02 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | -0.01 | -0.00 | -0.01 | -0.01 | 0.02 | 0.01 | 0.02 | -0.01 | -0.01 | -0.01 | -0.02 | -0.02 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | -0.00 | -0.02 | 0.01 | -0.00 | -0.00 | 0.01 | -0.02 | -0.02 | 0.01 | -0.01 | 0.00 | 0.01 | -0.02 | -0.01 | 0.04 | 0.01 | 0.02 | 0.04 | -0.01 | -0.01 | 0.03 | 0.00 | 0.02 | 0.03 | -0.01 | -0.01 | 0.04 | 0.00 | 0.02 | 0.04 | -0.01 | -0.01 | 0.04 | 0.00 | 0.02 | 0.03 | -0.01 | 0.02 | -0.00 | 0.02 | 0.01 | 0.02 | 0.00 | 0.02 | 0.01 | 0.02 | 0.01 | -0.01 |
| feature_7 | -0.01 | -0.02 | 0.03 | 0.03 | 0.02 | 0.02 | 0.02 | -0.02 | 0.12 | 0.08 | 0.37 | 0.36 | 0.28 | 0.25 | 1.00 | 0.90 | 0.20 | 0.16 | 0.59 | 0.53 | 0.38 | 0.33 | 0.24 | 0.20 | 0.40 | 0.37 | 0.05 | 0.05 | 0.18 | 0.20 | 0.10 | 0.10 | 0.05 | 0.05 | 0.49 | 0.43 | 0.10 | 0.07 | 0.29 | 0.25 | 0.19 | 0.16 | 0.11 | 0.09 | 0.23 | 0.23 | 0.28 | 0.26 | -0.07 | 0.12 | 0.09 | -0.02 | -0.05 | 0.05 | 0.10 | 0.06 | 0.03 | 0.00 | -0.02 | -0.05 | 0.16 | 0.06 | 0.01 | 0.02 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.03 | 0.03 | 0.01 | -0.01 | -0.01 | -0.03 | -0.03 | 0.15 | 0.05 | 0.11 | -0.01 | 0.01 | -0.00 | -0.00 | 0.00 | -0.02 | -0.01 | 0.01 | -0.00 | -0.00 | 0.00 | -0.01 | -0.02 | 0.06 | 0.00 | 0.02 | 0.05 | -0.01 | -0.05 | 0.04 | -0.03 | -0.01 | 0.02 | -0.05 | -0.01 | 0.05 | 0.01 | 0.03 | 0.04 | -0.00 | -0.05 | 0.03 | -0.03 | -0.00 | 0.01 | -0.05 | -0.00 | 0.11 | 0.02 | 0.05 | 0.10 | -0.01 | -0.05 | 0.06 | -0.02 | 0.01 | 0.04 | -0.05 | 0.13 | -0.00 | 0.14 | 0.03 | 0.14 | 0.01 | 0.14 | 0.02 | 0.14 | 0.03 | -0.01 |
| feature_8 | -0.00 | -0.00 | 0.03 | 0.03 | 0.01 | 0.01 | 0.01 | -0.01 | 0.08 | 0.09 | 0.34 | 0.40 | 0.25 | 0.28 | 0.90 | 1.00 | 0.14 | 0.18 | 0.53 | 0.60 | 0.33 | 0.38 | 0.19 | 0.22 | 0.37 | 0.43 | 0.04 | 0.05 | 0.18 | 0.24 | 0.09 | 0.12 | 0.04 | 0.07 | 0.42 | 0.46 | 0.07 | 0.07 | 0.26 | 0.27 | 0.16 | 0.18 | 0.09 | 0.10 | 0.21 | 0.25 | 0.24 | 0.27 | -0.05 | 0.04 | -0.01 | -0.01 | -0.04 | 0.02 | 0.04 | 0.03 | 0.03 | 0.00 | 0.01 | -0.04 | 0.09 | 0.08 | 0.01 | 0.02 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 | -0.02 | -0.01 | -0.03 | -0.03 | 0.11 | 0.08 | 0.13 | -0.00 | 0.01 | -0.00 | -0.00 | 0.00 | -0.01 | 0.00 | 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.06 | 0.02 | 0.04 | 0.06 | -0.01 | -0.04 | 0.03 | -0.01 | 0.01 | 0.03 | -0.05 | 0.00 | 0.05 | 0.02 | 0.04 | 0.05 | -0.01 | -0.04 | 0.03 | -0.01 | 0.01 | 0.02 | -0.05 | 0.01 | 0.11 | 0.03 | 0.06 | 0.10 | -0.01 | -0.03 | 0.06 | -0.00 | 0.02 | 0.05 | -0.05 | 0.06 | 0.02 | 0.08 | 0.06 | 0.06 | 0.04 | 0.07 | 0.05 | 0.07 | 0.05 | -0.00 |
| feature_9 | -0.05 | -0.06 | 0.04 | 0.04 | 0.03 | 0.02 | 0.02 | 0.03 | 0.72 | 0.55 | 0.05 | 0.04 | 0.04 | 0.03 | 0.20 | 0.14 | 1.00 | 0.83 | 0.34 | 0.26 | 0.57 | 0.42 | 0.86 | 0.70 | 0.18 | 0.14 | 0.39 | 0.31 | 0.24 | 0.19 | 0.30 | 0.24 | 0.35 | 0.29 | 0.10 | 0.08 | 0.28 | 0.22 | 0.16 | 0.13 | 0.22 | 0.18 | 0.24 | 0.21 | 0.09 | 0.07 | 0.02 | 0.02 | -0.39 | 0.57 | 0.42 | 0.00 | -0.20 | 0.24 | 0.53 | 0.32 | 0.16 | 0.06 | -0.06 | -0.16 | 0.67 | 0.19 | 0.07 | 0.05 | 0.07 | 0.07 | 0.05 | 0.02 | 0.02 | 0.02 | 0.03 | -0.02 | -0.04 | -0.04 | -0.05 | -0.05 | 0.77 | 0.31 | 0.58 | -0.01 | -0.05 | -0.02 | -0.03 | -0.04 | -0.04 | -0.01 | -0.04 | -0.01 | -0.02 | -0.04 | -0.02 | 0.08 | 0.15 | 0.10 | 0.12 | 0.13 | 0.06 | -0.17 | 0.01 | -0.12 | -0.08 | -0.01 | -0.19 | 0.10 | 0.21 | 0.13 | 0.16 | 0.20 | 0.07 | -0.17 | 0.08 | -0.10 | -0.04 | 0.03 | -0.18 | 0.12 | 0.40 | 0.14 | 0.21 | 0.35 | 0.07 | -0.16 | 0.15 | -0.11 | -0.04 | 0.07 | -0.18 | 0.57 | -0.02 | 0.61 | 0.05 | 0.59 | -0.00 | 0.61 | 0.01 | 0.61 | 0.03 | -0.05 |
| feature_10 | 0.00 | 0.02 | 0.03 | 0.03 | 0.02 | 0.01 | 0.01 | 0.03 | 0.58 | 0.67 | 0.05 | 0.05 | 0.03 | 0.03 | 0.16 | 0.18 | 0.83 | 1.00 | 0.27 | 0.32 | 0.47 | 0.51 | 0.71 | 0.84 | 0.14 | 0.16 | 0.32 | 0.37 | 0.19 | 0.22 | 0.25 | 0.27 | 0.30 | 0.34 | 0.08 | 0.10 | 0.24 | 0.28 | 0.13 | 0.16 | 0.19 | 0.22 | 0.21 | 0.27 | 0.07 | 0.08 | 0.02 | 0.03 | -0.28 | 0.23 | -0.04 | -0.01 | -0.21 | 0.11 | 0.25 | 0.21 | 0.18 | 0.05 | 0.04 | -0.16 | 0.41 | 0.30 | 0.04 | 0.05 | 0.05 | 0.05 | 0.04 | -0.00 | -0.00 | 0.02 | 0.02 | -0.03 | -0.05 | -0.04 | -0.06 | -0.06 | 0.61 | 0.48 | 0.72 | -0.00 | -0.04 | -0.01 | -0.03 | -0.04 | 0.00 | 0.00 | -0.03 | -0.01 | -0.02 | -0.03 | 0.02 | 0.06 | 0.19 | 0.10 | 0.15 | 0.17 | -0.01 | -0.20 | 0.03 | -0.13 | -0.07 | 0.00 | -0.26 | 0.07 | 0.23 | 0.13 | 0.17 | 0.22 | -0.01 | -0.21 | 0.08 | -0.11 | -0.05 | 0.03 | -0.26 | 0.10 | 0.45 | 0.14 | 0.23 | 0.40 | -0.00 | -0.20 | 0.15 | -0.13 | -0.04 | 0.08 | -0.25 | 0.28 | 0.08 | 0.34 | 0.17 | 0.30 | 0.11 | 0.32 | 0.13 | 0.34 | 0.15 | 0.01 |
| feature_11 | -0.02 | -0.03 | 0.04 | 0.04 | 0.02 | 0.02 | 0.02 | -0.01 | 0.22 | 0.15 | 0.24 | 0.23 | 0.18 | 0.16 | 0.59 | 0.53 | 0.34 | 0.27 | 1.00 | 0.90 | 0.64 | 0.56 | 0.41 | 0.34 | 0.35 | 0.32 | 0.12 | 0.10 | 0.38 | 0.39 | 0.23 | 0.21 | 0.13 | 0.12 | 0.38 | 0.34 | 0.12 | 0.09 | 0.45 | 0.39 | 0.26 | 0.24 | 0.14 | 0.12 | 0.17 | 0.17 | 0.18 | 0.17 | -0.13 | 0.21 | 0.15 | -0.02 | -0.08 | 0.08 | 0.18 | 0.11 | 0.05 | 0.01 | -0.02 | -0.07 | 0.25 | 0.08 | 0.02 | 0.03 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.01 | -0.02 | -0.01 | -0.03 | -0.03 | 0.26 | 0.09 | 0.19 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | -0.02 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | 0.00 | 0.07 | 0.01 | 0.03 | 0.06 | 0.00 | -0.07 | 0.03 | -0.05 | -0.03 | 0.01 | -0.07 | 0.01 | 0.08 | 0.02 | 0.05 | 0.08 | 0.01 | -0.07 | 0.04 | -0.04 | -0.01 | 0.02 | -0.07 | 0.02 | 0.16 | 0.04 | 0.08 | 0.14 | 0.01 | -0.07 | 0.08 | -0.04 | -0.00 | 0.05 | -0.07 | 0.21 | -0.01 | 0.23 | 0.04 | 0.22 | 0.00 | 0.22 | 0.02 | 0.23 | 0.03 | -0.02 |
| feature_12 | 0.00 | 0.00 | 0.03 | 0.02 | 0.02 | 0.01 | 0.01 | -0.00 | 0.16 | 0.19 | 0.21 | 0.26 | 0.16 | 0.17 | 0.53 | 0.60 | 0.26 | 0.32 | 0.90 | 1.00 | 0.57 | 0.64 | 0.33 | 0.39 | 0.32 | 0.36 | 0.10 | 0.11 | 0.35 | 0.44 | 0.20 | 0.24 | 0.11 | 0.14 | 0.33 | 0.37 | 0.10 | 0.10 | 0.40 | 0.43 | 0.23 | 0.27 | 0.12 | 0.14 | 0.16 | 0.19 | 0.16 | 0.19 | -0.09 | 0.09 | -0.01 | -0.01 | -0.08 | 0.04 | 0.08 | 0.07 | 0.06 | 0.01 | 0.01 | -0.07 | 0.16 | 0.12 | 0.01 | 0.03 | 0.01 | 0.02 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.01 | -0.02 | -0.02 | -0.04 | -0.03 | 0.20 | 0.15 | 0.24 | -0.00 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.00 | -0.01 | -0.01 | 0.00 | 0.01 | 0.09 | 0.03 | 0.05 | 0.08 | -0.01 | -0.07 | 0.03 | -0.04 | -0.01 | 0.02 | -0.09 | 0.01 | 0.09 | 0.03 | 0.06 | 0.09 | -0.01 | -0.07 | 0.04 | -0.03 | -0.00 | 0.03 | -0.09 | 0.03 | 0.18 | 0.05 | 0.10 | 0.16 | -0.00 | -0.07 | 0.08 | -0.03 | 0.01 | 0.06 | -0.09 | 0.10 | 0.02 | 0.13 | 0.08 | 0.11 | 0.04 | 0.12 | 0.05 | 0.13 | 0.07 | 0.00 |
| feature_13 | -0.03 | -0.04 | 0.04 | 0.03 | 0.02 | 0.02 | 0.02 | 0.02 | 0.39 | 0.29 | 0.14 | 0.14 | 0.11 | 0.09 | 0.38 | 0.33 | 0.57 | 0.47 | 0.64 | 0.57 | 1.00 | 0.88 | 0.67 | 0.57 | 0.28 | 0.25 | 0.23 | 0.19 | 0.36 | 0.34 | 0.40 | 0.36 | 0.25 | 0.22 | 0.24 | 0.21 | 0.17 | 0.13 | 0.35 | 0.30 | 0.37 | 0.34 | 0.19 | 0.17 | 0.14 | 0.13 | 0.11 | 0.10 | -0.23 | 0.34 | 0.24 | -0.01 | -0.13 | 0.14 | 0.31 | 0.19 | 0.10 | 0.03 | -0.04 | -0.11 | 0.40 | 0.12 | 0.04 | 0.03 | 0.04 | 0.04 | 0.03 | 0.02 | 0.02 | 0.03 | 0.03 | 0.00 | -0.03 | -0.02 | -0.04 | -0.03 | 0.45 | 0.17 | 0.33 | -0.01 | -0.03 | -0.01 | -0.03 | -0.03 | -0.03 | -0.01 | -0.03 | -0.01 | -0.02 | -0.02 | -0.01 | 0.03 | 0.10 | 0.04 | 0.05 | 0.09 | 0.02 | -0.11 | 0.03 | -0.08 | -0.05 | 0.01 | -0.12 | 0.04 | 0.14 | 0.06 | 0.09 | 0.13 | 0.03 | -0.11 | 0.07 | -0.06 | -0.02 | 0.03 | -0.11 | 0.06 | 0.26 | 0.07 | 0.13 | 0.23 | 0.03 | -0.11 | 0.12 | -0.07 | -0.01 | 0.07 | -0.11 | 0.35 | -0.02 | 0.37 | 0.04 | 0.36 | -0.00 | 0.36 | 0.01 | 0.37 | 0.03 | -0.03 |
| feature_14 | 0.00 | 0.01 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 | 0.02 | 0.28 | 0.32 | 0.13 | 0.16 | 0.09 | 0.10 | 0.33 | 0.38 | 0.42 | 0.51 | 0.56 | 0.64 | 0.88 | 1.00 | 0.54 | 0.63 | 0.24 | 0.27 | 0.17 | 0.20 | 0.32 | 0.39 | 0.35 | 0.40 | 0.20 | 0.24 | 0.21 | 0.24 | 0.13 | 0.14 | 0.31 | 0.34 | 0.33 | 0.39 | 0.16 | 0.20 | 0.12 | 0.14 | 0.09 | 0.11 | -0.15 | 0.13 | -0.02 | -0.01 | -0.12 | 0.06 | 0.13 | 0.11 | 0.10 | 0.02 | 0.02 | -0.09 | 0.23 | 0.18 | 0.02 | 0.04 | 0.03 | 0.03 | 0.03 | 0.01 | 0.01 | 0.03 | 0.03 | -0.00 | -0.03 | -0.02 | -0.04 | -0.04 | 0.32 | 0.24 | 0.38 | -0.00 | -0.02 | -0.01 | -0.02 | -0.02 | -0.00 | 0.00 | -0.02 | -0.00 | -0.01 | -0.02 | 0.01 | 0.03 | 0.11 | 0.06 | 0.08 | 0.11 | -0.00 | -0.10 | 0.03 | -0.06 | -0.02 | 0.02 | -0.14 | 0.04 | 0.14 | 0.07 | 0.10 | 0.14 | -0.00 | -0.11 | 0.06 | -0.05 | -0.01 | 0.04 | -0.14 | 0.06 | 0.26 | 0.08 | 0.15 | 0.24 | 0.00 | -0.10 | 0.10 | -0.05 | 0.01 | 0.07 | -0.13 | 0.16 | 0.04 | 0.19 | 0.11 | 0.17 | 0.06 | 0.18 | 0.07 | 0.19 | 0.09 | 0.00 |
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| feature_124 | -0.06 | -0.21 | 0.03 | 0.03 | 0.02 | 0.02 | 0.02 | 0.01 | 0.43 | 0.18 | 0.04 | 0.02 | 0.03 | 0.02 | 0.14 | 0.06 | 0.59 | 0.30 | 0.22 | 0.11 | 0.36 | 0.17 | 0.51 | 0.27 | 0.12 | 0.06 | 0.21 | 0.11 | 0.13 | 0.07 | 0.16 | 0.08 | 0.18 | 0.10 | 0.07 | 0.03 | 0.16 | 0.07 | 0.10 | 0.04 | 0.12 | 0.06 | 0.12 | 0.06 | 0.05 | 0.03 | 0.02 | 0.01 | -0.54 | 0.84 | 0.63 | 0.03 | -0.23 | 0.23 | 0.57 | 0.30 | 0.11 | -0.04 | -0.23 | -0.03 | 0.87 | 0.12 | 0.12 | 0.07 | 0.13 | 0.14 | 0.10 | -0.06 | -0.06 | -0.05 | -0.05 | -0.19 | -0.16 | -0.16 | -0.17 | -0.17 | 0.47 | -0.18 | 0.19 | -0.02 | -0.03 | -0.01 | -0.02 | -0.03 | -0.06 | -0.01 | -0.02 | -0.01 | -0.01 | -0.02 | -0.02 | 0.12 | 0.09 | 0.12 | 0.10 | 0.09 | 0.01 | -0.19 | -0.08 | -0.15 | -0.14 | -0.10 | -0.32 | 0.14 | 0.12 | 0.14 | 0.13 | 0.12 | 0.03 | -0.19 | -0.04 | -0.13 | -0.11 | -0.07 | -0.31 | 0.15 | 0.23 | 0.16 | 0.17 | 0.22 | 0.01 | -0.19 | -0.09 | -0.17 | -0.16 | -0.12 | -0.29 | 0.97 | 0.18 | 0.92 | 0.13 | 1.00 | 0.22 | 0.98 | 0.21 | 0.94 | 0.16 | -0.06 |
| feature_125 | -0.04 | -0.02 | 0.01 | 0.01 | 0.00 | -0.00 | -0.00 | -0.00 | -0.03 | 0.06 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.04 | -0.00 | 0.11 | 0.00 | 0.04 | -0.00 | 0.06 | 0.00 | 0.09 | 0.01 | 0.03 | 0.03 | 0.06 | 0.01 | 0.03 | 0.01 | 0.04 | 0.02 | 0.06 | 0.01 | 0.02 | 0.03 | 0.06 | 0.01 | 0.03 | 0.02 | 0.05 | 0.03 | 0.06 | 0.00 | 0.01 | 0.00 | 0.01 | 0.09 | -0.27 | -0.20 | -0.00 | 0.08 | -0.11 | -0.21 | -0.12 | -0.06 | -0.04 | -0.02 | 0.09 | 0.13 | 0.59 | 0.06 | 0.05 | 0.09 | 0.10 | 0.08 | -0.20 | -0.21 | -0.24 | -0.24 | -0.52 | -0.40 | -0.40 | -0.39 | -0.39 | -0.07 | 0.17 | 0.04 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.07 | -0.00 | 0.01 | -0.00 | 0.00 | 0.00 | 0.05 | 0.05 | -0.05 | 0.04 | 0.00 | -0.04 | -0.30 | 0.14 | -0.02 | 0.13 | 0.07 | 0.01 | -0.27 | 0.05 | -0.06 | 0.04 | -0.01 | -0.05 | -0.28 | 0.15 | -0.03 | 0.13 | 0.07 | 0.01 | -0.28 | 0.06 | -0.14 | 0.03 | -0.03 | -0.10 | -0.32 | 0.15 | -0.07 | 0.14 | 0.07 | -0.02 | -0.26 | 0.19 | 0.92 | 0.18 | 0.76 | 0.22 | 1.00 | 0.22 | 0.96 | 0.19 | 0.85 | -0.04 |
| feature_126 | -0.05 | -0.22 | 0.03 | 0.03 | 0.02 | 0.02 | 0.02 | 0.01 | 0.44 | 0.20 | 0.04 | 0.02 | 0.03 | 0.02 | 0.14 | 0.07 | 0.61 | 0.32 | 0.22 | 0.12 | 0.36 | 0.18 | 0.52 | 0.29 | 0.12 | 0.07 | 0.22 | 0.12 | 0.14 | 0.08 | 0.16 | 0.09 | 0.19 | 0.11 | 0.08 | 0.04 | 0.17 | 0.08 | 0.10 | 0.05 | 0.13 | 0.06 | 0.13 | 0.07 | 0.05 | 0.03 | 0.02 | 0.01 | -0.56 | 0.84 | 0.64 | 0.04 | -0.24 | 0.23 | 0.58 | 0.30 | 0.12 | -0.04 | -0.23 | -0.03 | 0.89 | 0.15 | 0.12 | 0.08 | 0.14 | 0.14 | 0.11 | -0.05 | -0.04 | -0.04 | -0.03 | -0.18 | -0.16 | -0.15 | -0.16 | -0.16 | 0.48 | -0.17 | 0.21 | -0.01 | -0.03 | -0.01 | -0.02 | -0.03 | -0.06 | -0.01 | -0.02 | -0.01 | -0.01 | -0.02 | -0.02 | 0.14 | 0.10 | 0.15 | 0.12 | 0.10 | 0.03 | -0.19 | -0.08 | -0.14 | -0.13 | -0.10 | -0.32 | 0.16 | 0.13 | 0.17 | 0.15 | 0.14 | 0.04 | -0.19 | -0.04 | -0.12 | -0.10 | -0.07 | -0.30 | 0.17 | 0.25 | 0.18 | 0.20 | 0.25 | 0.03 | -0.18 | -0.09 | -0.15 | -0.15 | -0.11 | -0.29 | 0.94 | 0.15 | 0.94 | 0.17 | 0.98 | 0.22 | 1.00 | 0.24 | 0.98 | 0.21 | -0.06 |
| feature_127 | -0.04 | -0.01 | 0.01 | 0.01 | 0.00 | -0.00 | 0.00 | 0.00 | -0.03 | 0.07 | 0.01 | 0.01 | 0.00 | 0.01 | 0.02 | 0.05 | 0.01 | 0.13 | 0.02 | 0.05 | 0.01 | 0.07 | 0.02 | 0.11 | 0.02 | 0.03 | 0.03 | 0.07 | 0.01 | 0.04 | 0.02 | 0.05 | 0.03 | 0.07 | 0.01 | 0.03 | 0.04 | 0.07 | 0.02 | 0.04 | 0.03 | 0.06 | 0.04 | 0.07 | 0.01 | 0.01 | 0.00 | 0.01 | 0.09 | -0.27 | -0.20 | 0.01 | 0.09 | -0.10 | -0.21 | -0.11 | -0.05 | -0.03 | -0.01 | 0.09 | 0.16 | 0.64 | 0.06 | 0.06 | 0.09 | 0.11 | 0.09 | -0.16 | -0.16 | -0.20 | -0.20 | -0.45 | -0.36 | -0.36 | -0.34 | -0.34 | -0.06 | 0.17 | 0.04 | 0.02 | 0.00 | 0.01 | 0.00 | 0.00 | 0.07 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.04 | 0.07 | -0.05 | 0.07 | 0.03 | -0.02 | -0.26 | 0.17 | -0.01 | 0.17 | 0.11 | 0.03 | -0.22 | 0.07 | -0.05 | 0.08 | 0.02 | -0.03 | -0.24 | 0.17 | -0.02 | 0.17 | 0.11 | 0.03 | -0.23 | 0.08 | -0.13 | 0.07 | 0.01 | -0.08 | -0.28 | 0.17 | -0.05 | 0.18 | 0.12 | 0.01 | -0.21 | 0.15 | 0.83 | 0.22 | 0.84 | 0.21 | 0.96 | 0.24 | 1.00 | 0.24 | 0.93 | -0.04 |
| feature_128 | -0.05 | -0.21 | 0.04 | 0.03 | 0.02 | 0.02 | 0.02 | 0.02 | 0.44 | 0.20 | 0.04 | 0.02 | 0.03 | 0.02 | 0.14 | 0.07 | 0.61 | 0.34 | 0.23 | 0.13 | 0.37 | 0.19 | 0.53 | 0.30 | 0.12 | 0.07 | 0.23 | 0.13 | 0.14 | 0.09 | 0.17 | 0.10 | 0.19 | 0.11 | 0.08 | 0.04 | 0.18 | 0.09 | 0.11 | 0.06 | 0.13 | 0.07 | 0.13 | 0.08 | 0.06 | 0.03 | 0.02 | 0.01 | -0.54 | 0.81 | 0.62 | 0.04 | -0.23 | 0.23 | 0.56 | 0.30 | 0.12 | -0.03 | -0.22 | -0.03 | 0.92 | 0.22 | 0.12 | 0.08 | 0.13 | 0.14 | 0.11 | -0.03 | -0.03 | -0.03 | -0.02 | -0.15 | -0.14 | -0.14 | -0.15 | -0.15 | 0.47 | -0.16 | 0.21 | -0.01 | -0.03 | -0.01 | -0.02 | -0.03 | -0.05 | -0.01 | -0.02 | -0.01 | -0.02 | -0.02 | -0.02 | 0.14 | 0.10 | 0.16 | 0.14 | 0.11 | 0.04 | -0.17 | -0.07 | -0.12 | -0.10 | -0.08 | -0.29 | 0.16 | 0.14 | 0.18 | 0.17 | 0.15 | 0.05 | -0.17 | -0.03 | -0.10 | -0.07 | -0.05 | -0.28 | 0.18 | 0.25 | 0.19 | 0.22 | 0.26 | 0.04 | -0.17 | -0.07 | -0.13 | -0.12 | -0.09 | -0.27 | 0.90 | 0.13 | 0.98 | 0.26 | 0.94 | 0.19 | 0.98 | 0.24 | 1.00 | 0.28 | -0.05 |
| feature_129 | -0.04 | -0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | -0.03 | 0.07 | 0.01 | 0.02 | 0.01 | 0.01 | 0.03 | 0.05 | 0.03 | 0.15 | 0.03 | 0.07 | 0.03 | 0.09 | 0.04 | 0.13 | 0.02 | 0.04 | 0.05 | 0.08 | 0.02 | 0.05 | 0.03 | 0.06 | 0.05 | 0.08 | 0.02 | 0.04 | 0.05 | 0.09 | 0.03 | 0.05 | 0.04 | 0.08 | 0.05 | 0.09 | 0.01 | 0.02 | 0.01 | 0.01 | 0.10 | -0.26 | -0.20 | 0.01 | 0.09 | -0.09 | -0.19 | -0.10 | -0.04 | -0.01 | 0.01 | 0.09 | 0.21 | 0.73 | 0.05 | 0.07 | 0.08 | 0.11 | 0.10 | -0.12 | -0.12 | -0.16 | -0.16 | -0.37 | -0.30 | -0.30 | -0.29 | -0.28 | -0.06 | 0.17 | 0.04 | 0.02 | 0.00 | 0.01 | 0.00 | 0.00 | 0.06 | 0.00 | -0.00 | -0.00 | -0.01 | -0.01 | 0.04 | 0.08 | -0.04 | 0.09 | 0.07 | -0.00 | -0.21 | 0.18 | 0.01 | 0.20 | 0.16 | 0.06 | -0.16 | 0.08 | -0.04 | 0.10 | 0.06 | -0.01 | -0.21 | 0.18 | 0.00 | 0.20 | 0.16 | 0.07 | -0.17 | 0.09 | -0.10 | 0.09 | 0.06 | -0.05 | -0.23 | 0.18 | -0.02 | 0.22 | 0.18 | 0.06 | -0.16 | 0.10 | 0.72 | 0.28 | 0.95 | 0.16 | 0.85 | 0.21 | 0.93 | 0.28 | 1.00 | -0.04 |
| ts_id | 1.00 | 0.03 | -0.01 | -0.01 | -0.01 | -0.01 | -0.01 | 0.00 | -0.03 | 0.02 | -0.00 | -0.00 | -0.01 | -0.01 | -0.01 | -0.00 | -0.05 | 0.01 | -0.02 | 0.00 | -0.03 | 0.00 | -0.04 | 0.01 | -0.01 | 0.00 | -0.02 | -0.00 | -0.01 | -0.00 | -0.02 | -0.00 | -0.02 | -0.01 | -0.01 | -0.00 | -0.03 | -0.01 | -0.01 | -0.00 | -0.02 | -0.01 | -0.02 | -0.01 | -0.00 | -0.00 | -0.00 | -0.00 | 0.03 | -0.03 | -0.13 | -0.08 | -0.14 | -0.05 | -0.06 | -0.02 | 0.01 | -0.05 | 0.01 | -0.01 | -0.06 | -0.04 | -0.09 | -0.05 | -0.08 | -0.08 | -0.07 | -0.02 | -0.02 | -0.01 | -0.01 | -0.03 | -0.02 | -0.02 | -0.03 | -0.03 | -0.03 | -0.01 | 0.03 | -0.00 | -0.01 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.01 | -0.01 | 0.01 | 0.00 | 0.00 | 0.01 | -0.02 | -0.09 | -0.03 | -0.06 | -0.05 | -0.03 | -0.10 | -0.01 | 0.02 | -0.00 | 0.01 | 0.02 | -0.02 | -0.09 | -0.02 | -0.06 | -0.05 | -0.03 | -0.10 | -0.01 | 0.03 | 0.00 | 0.01 | 0.03 | -0.03 | -0.09 | -0.04 | -0.07 | -0.06 | -0.05 | -0.10 | -0.06 | -0.04 | -0.05 | -0.04 | -0.06 | -0.04 | -0.06 | -0.04 | -0.05 | -0.04 | 1.00 |
# Features correlation with respect to resp only
pd.DataFrame(df_train_corr['resp']).sort_values('resp',ascending = False).style.background_gradient(cmap='YlGnBu')
| resp | |
|---|---|
| resp | 1.000000 |
| resp_4 | 0.956197 |
| resp_3 | 0.815972 |
| resp_2 | 0.595274 |
| resp_1 | 0.452159 |
| feature_27 | 0.048293 |
| feature_31 | 0.047021 |
| feature_39 | 0.043932 |
| feature_33 | 0.041301 |
| feature_35 | 0.033564 |
| feature_28 | 0.032502 |
| feature_29 | 0.030466 |
| feature_32 | 0.029504 |
| feature_40 | 0.028748 |
| feature_34 | 0.023818 |
| feature_7 | 0.021207 |
| feature_53 | 0.021034 |
| feature_11 | 0.020725 |
| feature_122 | 0.020313 |
| feature_128 | 0.019902 |
| feature_1 | 0.019802 |
| feature_126 | 0.019669 |
| feature_124 | 0.019478 |
| feature_13 | 0.019412 |
| feature_36 | 0.019326 |
| feature_120 | 0.018552 |
| feature_69 | 0.018534 |
| feature_9 | 0.018368 |
| feature_42 | 0.018267 |
| feature_15 | 0.018183 |
| feature_30 | 0.017356 |
| feature_43 | 0.015688 |
| feature_8 | 0.014660 |
| feature_101 | 0.014392 |
| feature_113 | 0.013843 |
| feature_44 | 0.013619 |
| feature_96 | 0.013469 |
| feature_89 | 0.013273 |
| feature_108 | 0.013209 |
| feature_12 | 0.012481 |
| feature_79 | 0.011976 |
| feature_2 | 0.011883 |
| feature_84 | 0.011500 |
| feature_14 | 0.010752 |
| feature_73 | 0.010445 |
| feature_71 | 0.010297 |
| feature_10 | 0.010188 |
| feature_85 | 0.009896 |
| feature_91 | 0.009741 |
| feature_16 | 0.009508 |
| feature_82 | 0.008672 |
| feature_110 | 0.008643 |
| feature_98 | 0.008454 |
| feature_88 | 0.007700 |
| feature_76 | 0.007584 |
| feature_56 | 0.007423 |
| feature_86 | 0.007228 |
| feature_59 | 0.006887 |
| feature_55 | 0.006565 |
| feature_58 | 0.006430 |
| feature_57 | 0.005959 |
| feature_107 | 0.005761 |
| feature_119 | 0.005590 |
| feature_87 | 0.005486 |
| feature_111 | 0.005089 |
| feature_47 | 0.004869 |
| feature_5 | 0.004814 |
| feature_94 | 0.004809 |
| feature_54 | 0.004621 |
| feature_102 | 0.004613 |
| feature_95 | 0.004548 |
| feature_114 | 0.004385 |
| feature_81 | 0.003926 |
| feature_112 | 0.003753 |
| feature_3 | 0.003608 |
| feature_90 | 0.003604 |
| feature_75 | 0.002835 |
| feature_99 | 0.002824 |
| feature_63 | 0.002754 |
| feature_70 | 0.002682 |
| feature_62 | 0.002421 |
| feature_116 | 0.001978 |
| feature_123 | 0.001857 |
| feature_109 | 0.001766 |
| feature_6 | 0.001706 |
| feature_104 | 0.001637 |
| feature_92 | 0.001140 |
| feature_60 | 0.001021 |
| feature_129 | 0.000985 |
| feature_93 | 0.000954 |
| feature_61 | 0.000943 |
| feature_4 | 0.000500 |
| feature_45 | 0.000288 |
| feature_127 | 0.000084 |
| feature_78 | 0.000072 |
| feature_80 | 0.000002 |
| feature_64 | -0.000387 |
| feature_117 | -0.000406 |
| feature_74 | -0.000408 |
| feature_46 | -0.000490 |
| feature_67 | -0.000993 |
| feature_68 | -0.001200 |
| feature_125 | -0.001211 |
| feature_48 | -0.001442 |
| feature_66 | -0.001547 |
| feature_121 | -0.001682 |
| feature_65 | -0.001783 |
| feature_118 | -0.001882 |
| feature_72 | -0.002034 |
| feature_105 | -0.002306 |
| feature_100 | -0.002728 |
| feature_115 | -0.002743 |
| feature_49 | -0.004349 |
| feature_83 | -0.006124 |
| feature_20 | -0.006614 |
| feature_50 | -0.006891 |
| weight | -0.006948 |
| ts_id | -0.007526 |
| date | -0.007590 |
| feature_106 | -0.007671 |
| feature_77 | -0.008028 |
| feature_97 | -0.008253 |
| feature_52 | -0.008280 |
| feature_41 | -0.008511 |
| feature_26 | -0.009957 |
| feature_51 | -0.010348 |
| feature_103 | -0.010920 |
| feature_19 | -0.012886 |
| feature_24 | -0.015145 |
| feature_22 | -0.016168 |
| feature_18 | -0.017448 |
| feature_25 | -0.018248 |
| feature_38 | -0.020683 |
| feature_0 | -0.023726 |
| feature_23 | -0.024656 |
| feature_21 | -0.027753 |
| feature_17 | -0.028277 |
| feature_37 | -0.029281 |
Just in case you also happended to be interested in the volumes Note that the return was relatively stable for a short while between 100 and 200 for some unknown reasons.
#Visualization: Daily Return vs Daily Volume
Volume = df_train.date
Volume = Volume.value_counts().sort_index()
daily_return = df_train[['date','resp']].groupby(['date']).sum()
daily_return
plt.rcParams["figure.figsize"] = (30,8)
ax_return = plt.subplot2grid((5,4),(0,0),rowspan = 3,colspan = 4)
ax_volumes = plt.subplot2grid((5,4),(3,0),colspan = 4,rowspan = 2)
ax_return.plot(daily_return.index, daily_return.resp, label = "Return")
ax_return.set_title("Return and Volume",fontsize = 30)
ax_return.legend(fontsize = 20)
ax_return.set_xlabel('Time',fontsize = 20)
ax_return.set_ylabel('Return',fontsize = 20)
ax_return.tick_params(axis = 'both',labelsize = 16)
plt.subplots_adjust(wspace = 0.5,hspace = 0.5)
ax_volumes.set_ylabel('Volume',fontsize = 20)
ax_volumes.bar(Volume.index, Volume, color = 'red',alpha = 0.7)
ax_volumes.tick_params(axis = 'both',labelsize = 16)
daily_return.describe()
| resp | |
|---|---|
| count | 500.000000 |
| mean | 1.952129 |
| std | 11.085616 |
| min | -48.649796 |
| 25% | -2.616761 |
| 50% | 1.187239 |
| 75% | 5.285396 |
| max | 57.957487 |
pd.DataFrame(Volume.describe())
| date | |
|---|---|
| count | 500.000000 |
| mean | 4780.982000 |
| std | 2023.246691 |
| min | 29.000000 |
| 25% | 3621.000000 |
| 50% | 4353.500000 |
| 75% | 5220.250000 |
| max | 18884.000000 |
Other competitioners are not talking about / using this file that much on Kaggle.
Each feature is consist of 28 tags.
No information in regards of tags are given.
Some features are suspected to be duplicates since they have exactly the same tags structure. However, those features don't hold the same values or distributions, therefore tags are not primary keys to features(meaning we can't distinguish features by just looking at their tags.)
df_feature = pd.read_csv('features.csv')
df_feature.head()
| feature | tag_0 | tag_1 | tag_2 | tag_3 | tag_4 | tag_5 | tag_6 | tag_7 | tag_8 | ... | tag_19 | tag_20 | tag_21 | tag_22 | tag_23 | tag_24 | tag_25 | tag_26 | tag_27 | tag_28 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | feature_0 | False | False | False | False | False | False | False | False | False | ... | False | False | False | False | False | False | False | False | False | False |
| 1 | feature_1 | False | False | False | False | False | False | True | True | False | ... | False | False | False | False | False | False | False | False | False | False |
| 2 | feature_2 | False | False | False | False | False | False | True | True | False | ... | False | False | False | False | False | False | False | False | False | False |
| 3 | feature_3 | False | False | False | False | False | False | True | False | True | ... | False | False | False | False | False | False | False | False | False | False |
| 4 | feature_4 | False | False | False | False | False | False | True | False | True | ... | False | False | False | False | False | False | False | False | False | False |
5 rows × 30 columns
#Duplicated features (in terms of tags)
feature_dup = df_feature.drop(['feature'], axis = 1).duplicated(subset=None, keep='first')
feature_dup[feature_dup == True]
42 True 43 True 48 True 50 True 51 True 52 True 61 True 63 True 65 True 66 True 67 True 68 True dtype: bool
# Features that has same tags
duplicated = df_feature.loc[feature_dup[feature_dup == True].index]
duplicated
| feature | tag_0 | tag_1 | tag_2 | tag_3 | tag_4 | tag_5 | tag_6 | tag_7 | tag_8 | ... | tag_19 | tag_20 | tag_21 | tag_22 | tag_23 | tag_24 | tag_25 | tag_26 | tag_27 | tag_28 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 42 | feature_42 | False | False | False | False | False | False | False | False | False | ... | False | False | False | False | False | False | False | False | False | False |
| 43 | feature_43 | False | False | False | False | False | False | False | False | False | ... | False | False | False | False | False | False | False | False | False | False |
| 48 | feature_48 | False | False | False | False | False | False | False | False | False | ... | True | False | False | False | False | False | False | False | False | False |
| 50 | feature_50 | False | False | False | False | False | False | False | False | False | ... | True | False | False | False | False | False | False | False | False | False |
| 51 | feature_51 | False | False | False | False | False | False | False | False | False | ... | True | False | False | False | False | False | False | False | False | False |
| 52 | feature_52 | False | False | False | False | False | False | False | False | False | ... | True | False | False | False | False | False | False | False | False | False |
| 61 | feature_61 | False | False | False | False | False | False | False | False | False | ... | False | False | False | True | False | False | False | False | False | False |
| 63 | feature_63 | False | False | False | False | False | False | False | False | False | ... | False | False | False | True | False | False | False | False | False | False |
| 65 | feature_65 | False | False | False | False | False | False | False | False | False | ... | False | False | False | True | False | False | False | False | False | False |
| 66 | feature_66 | False | False | False | False | False | False | False | False | False | ... | False | False | False | True | False | False | False | False | False | False |
| 67 | feature_67 | False | False | False | False | False | False | False | False | False | ... | False | False | False | True | False | False | False | False | False | False |
| 68 | feature_68 | False | False | False | False | False | False | False | False | False | ... | False | False | False | True | False | False | False | False | False | False |
12 rows × 30 columns
Again, the goal of this game is to maximize the utility score, in order to do that we need to make sure that we have right features to train the right model. At this point, the problems we need to tackle/discuss are:
1. Decide action value. Are we simply go with action = 1 when resp > 0 and action = 0 otherwise or is there any other thoughts that you guys may have?
2. How do we handle the missing values in this case? Drop them/assign 0 / assign 999/ others?
3. Most importantly, how do we select our features?
A couple of my points: